So a sample out of the entire shipment is selected The compa

So, a sample out of the entire shipment is selected. The company randomly selects 30 packages and determine whether each is within spec- ifications as some cookies could be broken, have an off taste, or not have enough chocolate chips! The entire shipment contains 1200 packages and only 2% of those packages do not meet specification. When looking at the sample of 30 packages, the shipment is cleared and accepted if there are at most 2 defects (meaning if there are 0,1, or 2 defects). a) Show that this problem can be handled using a binomial probability distribution. b) What is the probability that the shipment will be accepted? c) Are most of the shipments going to be accepted? Explain.

Solution

let X be the number of defects in the sample.

a) now the sample contains 30 packages. 2% of the entire shipment packages do not meet specifications. moreover the packages are made independent of each other.

So X can be treated as a binomial distribution.

X~Bin(30,0.02)

b)P[shipment is accepted]=P[X<=2]=P[X=0]+P[X=1]+P[X=2]=0.978282 [using minitab]   [answer]

c) so as seen from part b) that the probability of accepting the shipment is 0.978282 which is very high.

so most of the shipments are going to be accpeted. actually 97.8282% of the shipments are going to be accepted.